Entropy transfer efficiency-effectiveness method for heat exchangers, part 1: Local entropy generation number and operation performance limits

Here, to resolve the open problem of the second-law efficiency evaluation for heat exchangers, an efficiency-effectiveness method is developed from pure convection theory, where the entropy transfer efficiency defined as the outlet temperature ratio of cold and hot fluids exchanging entropy and local entropy generation number can measure the global and local irreversibilities of heat transfer. The efficiency and effectiveness are related by the inlet temperature ratio τ and capacity rate ratio φ, and their maxima subject to the local entropy generation number are determined for different flow arrangements. When τ = φ2, the effectiveness maxima are 0.5/(1 + φ) and 1/(1 + φ) while the highest efficiencies are φ and unity for parallelflow and counterflow arrangements, respectively. The optimum operating points of counterflow exchangers, at which the equal outlet temperature τT1∞ (T1∞ represents the hot inlet temperature) of two fluids with a critical capacity rate ratio τ induces uniform irreversibility, the effectiveness limit of 1/(1+τ), and the efficiency limit of unity, are obtained. A linear temperature difference method is also developed based on the redefined convective and overall heat transfer coefficients, invariably yielding an effectiveness equal to the number of heat transfer units. This method has potentials to be extended to wet heat exchangers with phase-change flows.